Question: Simplify the following expression: $r = \dfrac{x}{7} + \dfrac{x}{5}$
In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $7$ and $5$ $\lcm(7, 5) = 35$ $ r = \dfrac{5}{5} \cdot \dfrac{x}{7} + \dfrac{7}{7} \cdot \dfrac{x}{5} $ $r = \dfrac{5x}{35} + \dfrac{7x}{35}$ $r = \dfrac{5x +7x}{35}$ $r = \dfrac{12x}{35}$